The bipolaron theory of high-temperature superconductors

An outline is given for the bipolaron theory of high-temperature superconductivity, both for the cubic bismuth oxide and the copper oxide materials. It is emphasized that the BCS theory takes this form for strong interaction. The possible role of spin polarons in the latter is also discussed.     

过苯胺黑聚合物的双极化子态

利用改进的Ginder-Epstein模型研究聚苯胺黑的双极化子态, 给出其键序波幅、芳环扭角、电子能级、理论吸收谱和电荷分布,并与极化子进行对比。结果发现双极化子激发能为3.08eV, 晶格驰豫宽度涉及12格点与极化子相当;键交错驰豫深度大约为极化子的2倍,畸变中心芳环扭角高达68.35°大于极化子中心扭角的2倍。两个能隙态几乎简并,吸收谱低能峰为1.6eV。     

Computer simulation study of bipolaron formation

Monte Carlo computer simulation techniques are used to study the formation of bipolarons on a lattice. The transition between the three possible states, extended, twopolaron, and bipolaron is studied. The phase diagram as a function of the strengths of the electron-phonon coupling and repulsive interaction is determined.     

过苯胺黑聚合物的双极化子态

利用改进的Ginder-Epstein模型研究聚苯胺黑的双极化子态,给出其键序波幅、芳环扭角、电子能级、理论吸收谱和电荷分布,并与极化子进行对比.结果发现双极化子激发能为3.08 eV,晶格驰豫宽度涉及12格点与极化子相当;键交错驰豫深度大约为极化子的2倍,畸变中心芳环扭角高达68.35°大于极化子中心扭角的2倍.两个能隙态几乎简并,吸收谱低能峰为1.6 eV.     

Electron correlations and instability of a two-center bipolaron

The energy of a large bipolaron is calculated for various spacings between the centers of the polarization potential wells of the two polarons with allowance made for electron correlations (i.e., the explicit dependence of the wave function of the system on the distance between the electrons) and for permutation symmetry of the two-electron wave function. The lowest singlet and triplet 2³S states of the bipolaron are considered. The singlet polaron is shown to be stable over the range of ionic-bond parameter values η≤η_m≈0.143 (η=?_∞/?₀, where ?_∞ and ?₀ are the high-frequency and static dielectric constants, respectively). There is a single energy minimum, corresponding to the single-center bipolaron configuration (similar to a helium atom). The binding energy of the bipolaron for η → 0 is J_bp=?0.136512e⁴m^*/?²? _∞ ² (e and m* are the charge and effective mass of a band electron), or 25.8% of the double polaron energy. The triplet bipolaron state (similar to an orthohelium atom) is energetically unfavorable in the system at hand. The single-center configuration of the triplet bipolaron corresponds to a sharp maximum in the distance dependence of the total energy J_bp(R); therefore, a transition of the bipolaron to the orthostate (e.g., due to exchange scattering) will lead to decay of the bound two-particle state. The exchange interaction between polarons is antiferromagnetic (AFM) in character. If the conditions for the Wigner crystallization of a polaron gas are met, the AFM exchange interaction between polarons can lead to AFM ordering in the system of polarons.     

Spatial configuration of the bipolaron and the virial theorem

The conditions of the virial theorem imposed on the dependence of the total energy of a system consisting of two polarons on the distance between the centers of the polarization wells are analyzed for various trial two-electron functions in the limit of strong electron-phonon coupling. It is shown that the inclusion of the direct dependence of the wave function of the system on the interelectron distance (correlation effects) does not break the conditions of the virial theorem. This theorem holds for a single-center and a two-center configuration corresponding to a subsidiary minimum, which disappears when the electron correlations are included.     

The region of existence of the three-dimensional continuum bipolaron

The ranges of ?^*/?_∞ and of the electron-phonon coupling constant in which the three-dimensional bipolaron exists are determined. The limits of these ranges correspond to the emergence of the first bound state of two polarons. The criteria for the first bound state to arise are found by solving an integral equation, which corresponds to a Schrödinger equation describing internal vibrations of a bipolaron. The Hamiltonian describing these vibrations is separated from the complete Hamiltonian of the electron-phonon system by using the Bogoliubov-Tyablikov method of canonical transformations of coordinates.     

Hartree-Fock approximation of bipolaron state in quantum dots and wires

The bipolaronic ground state of two electrons in a spherical quantum dot or a quantum wire with parabolic boundaries is studied in the strong electron-phonon coupling regime. We introduce a variational wave function that can conveniently conform to represent alternative ground state configurations of the two electrons, namely, the bipolaronic bound state, the state of two individual polarons, and two nearby interacting polarons confined by the external potential. In the bipolaron state the electrons are found to be separated by a finite distance about a polaron size. We present the formation and stability criteria of bipolaronic phase in confined media. It is shown that the quantum dot confinement extends the domain of stability of the bipolaronic bound state of two electrons as compared to the bulk geometry, whereas the quantum wire geometry aggravates the formation of stable bipolarons.     

Ground state and polaron and bipolaron excited states in polydiacetylene

The electronic properties of ground state and charged excited states of non-degenerate polydiacetylene were investigated by means of a tight-binding model. The parameters of the model were obtained by comparison of the experimental and other theoretical results. It was found that there is a stable dimerized structure of polydiacetylene in ground state and the doping induces the nonlinear excitations, such as polarons and bipolarons. In order to compare the stability of polaron and bipolaron, the creation energy and binding energy were separately defined. By neglecting the electron-electron Coulomb interaction, a bipolaron is more stable than two independent polarons.     

Low-temperature anharmonic vibrations in the cuprates: a bipolaron model

Il Nuovo Cimento D - Starting from the recent experiments that have revealed large-amplitude anharmonic vibrations in the cuprates, the possibility of formation of bipolarons has been investigated....     

Energy and critical ionic-bond parameter of a 3D large-radius bipolaron

A theory of a strong-coupling large-radius bipolaron has been developed. The possibility of the formation of 3D bipolarons in high-temperature superconductors is discussed. For the bipolaron energy, the lowest variational estimate has been obtained at α > 8, where α is the electron-phonon coupling constant. The critical ionic-bond parameter η _c = ɛ_∞/ɛ₀, where ɛ_∞ and ɛ₀ are the high-frequency and static dielectric constants, has been found to be η _c = 0.2496.     

Temperature dependence of the properties of strong-coupling bipolaron in a quantum dot

Temperature dependence of the properties of strong-coupling bipolaron in a quantum dot (QD) is studied based on the Lee-Low-Pines-Huybrechts variational method and quantum statistical theory. Results of the numerical calculation show that the vibration frequency as well as the absolute value of the induced potential and the effective potential all increase with increasing coupling strength and temperature, respectively, and they also increase with decreasing relative distance of electrons. The bipolarons are closer and more stable when the temperature is higher and coupling strength is larger. The influence of radius of QD and dielectric constant ratio on the effective potential is little.     

钉扎效应对聚噻吩中双空穴极化子附近局域振动模的影响

基于扩展的二维Su-Schrieffer-Heeger模型，研究了库仑钉扎作用对聚噻吩中双空穴极化子 附近的局域振动模的影响.除了与激发方式无关的本征振动模外，发现了与激发方式相关的 声子振动模式.计算结果与聚噻吩红外和拉曼光谱实验数据相当符合，从而对掺杂诱导和光 致激发下聚噻吩吸收光谱的区别给出了较好的理论阐释. 关键词： 聚噻吩 钉扎效应 吸收光谱 局域振动模     

Dissociation of bipolaron in non-degenerate polymer chain at high electric fields

We investigate the dynamics of bipolaron in non-degenerate polymer (e.g. PPV) in an external electric field by using a nonadiabatic evolution method, which allows transition between instantaneous electronic states. When the applied electric field exceeds a critical value, a bipolaron is found to dissociate like the case of polaron due to the lattice distortion not being able to follow the fast moving electrons. The critical value is estimated to be of order ¹⁰⁶ V/cm${10}^6\text{ V}/\text{cm}$. This result is consistent with experiment in that a large increase in current in PPV occurs at high fields. At a given electric field, the saturation velocity of bipolaron will decrease with the increase of non-degenerate parameters te$t_e$.     

Formation dynamics of bipolaron in a metal/polymer/metal structure

Charge injection process from metal electrode to a nondegenerate polymer in a metal/ polymer/ metal structure has been investigated by using a nonadiabatic dynamic method. We demonstrate that the dynamical formation of a bipolaron sensitively depends on the strength of applied electric field, the work function of metal electrode, and the contact between the polymer and the electrode. For a given bias applied to one of the electrode (V₀) and coupling between the electrode and the polymer (t^′), such as V₀=0.79 eV and t^′=1 eV, the charge injection process depending on the electric field can be divided into the following three cases: (1) in the absence of the electric field, only one electron tunnels into the polymer to form a polaron near the middle of the polymer chain; (2) at low electric fields, two electrons transfer into the polymer chain to form a bipolaron; (3) at higher electric fields, bipolaron can not be formed in the polymer chain, electrons are transferred from the left electrode to right electrode through the polymer one by one accompanying with small irregular lattice deformations.